(This
exercise has been modified from one developed by J. A. Holmes of the University
of Toronto)

Knowledge of depth, sediment area, area of water strata at various
depths, volumes of strata between depth contours, shoreline characteristics and
other morphological features of a lake or stream is important because the
morphology affects nearly all major physical, chemical, and biological
properties that we measure in lakes.For
example, information on morphometry is needed to investigate erosion, nutrient
loading rates, chemical mass, heat content, thermal stability, biological
productivity and growth, and other ecosystem structures and function in lakes.

Hayes and Anthony (1964) found that for 150 North American lakes, fish
productivity could be directly related to mean depth and surface area.
Schindler (1971) explained differences in the trophic status among a group of
neighboring lakes in Ontario by differences in surface area, lake volume, and
drainage area.

The
morphology of a lake or stream tends to reflect its geological origins. Most
lakes in Pennsylvania were formed as a result of glaciation, either by glacial
scouring or meltwater flows, or a block of melting ice (kettle lakes). Some
useful parameters that you will be measuring and calculating are shown below.
All of these parameters can be measured and calculated from topographic or
hydrographic (showing lake bottom, i.e., depth contours) maps and should be
completed before beginning work on a lake.

1.
Lake surface area (Ao) is measured by digitizer or polar planimeter.

2. If
you are lucky, lake volume (V) is calculated from bathymetric
map. If not, you may have to construct your own by making soundings
(most easily done on frozen lakes) or using a 'fish-finder' to scan the
bottom.

Consider the lake as
an irregularly shaped cone, divided into segments by the different depth
contours. The upper and lower surfaces of each segment are delineated by
sequential depth contours. The volume of the lake is calculated by summing the
"surface area" of each depth contour and applying the formula for the
volume of a cone. Thus, if there are two depth contours, the volume is
calculated as

V
= h/3[A1 + A2 + Ö(
A1 x A2)]

where
h is the difference between depth contours, A1 is the
area of the upper depth contour, and A2 is the area of the
lower contour. The last or bottom cone is calculated as

Volume
= 1.047 x r2 x h

where
r is the radius of the top of the cone and h is the depth, i.e.,
the difference between the last depth contour (top of the cone) and the maximum
depth.

3.
Limnological mean depth (˛) = V/Ao

4.
Maximum depth (zmax) taken from bathymetric map.

5.
Relative depth (zr) expresses the zmax as a
percentage of the mean diameter of the lake. Most lakes have a zr
< 2%. Some deep lakes with small surface areas may have zr
values > 4% and these lakes tend to exhibit greater stability than those with
a lower zr.

zr
= 50 x zmaxx √π/√Ao

6.
Mean depth:maximum depth ratio (˛: zmax) provides
information on how lake shape differs from a cone and it describes the form of a
basin relative to the development of its volume. A cone has a ratio of 0.33.
Lakes with deep holes such as kettle lakes have values < 0.33. Fjord-type
lakes have ratios > 0.5 while most lakes in Pennsylvania will have ratios
between 0.33 and 0.5.

7.
Fetch is the maximum distance on a lake surface between any two unobstructed
points. This parameter is important for predicting wave height and thermocline
depth.

8.
Shoreline length (L) is a linear distance and is measured using a
cartographic wheel.

9.
Shoreline development (DL) is the degree of shoreline
irregularity expressed as ratio of L to circumference of a circle of area
equal to Ao. The closer this ratio is to 1, the more circular the lake. A larger
ratio means the shoreline is more crenulated and hence the potential for
littoral community development is greater. Shoreline development is calculated
as

DL
= L / (2 x √π x Ao

10. A
hypsographic or depth-area curve describes the relationship between surface area
and depth. The curve is plotted on graph paper and may be expressed in relative
(%) or absolute units (m2, ha, km2). This curve only
approximates the area of exposed lake bottom sediments between depth contours
since areal measurements are related to the plane of the lake surface.

11.
Drainage basin is the total land surface area drained by tributaries that feed
the main channel of a stream.This
parameter is calculated for streams or lakes by outlining the height of land on
a topographic map and using a polar planimeter of digitizer. The term watershed
denotes the boundary between adjacent drainage basins and in practice it is used
as a synonym of drainage basin.

Laboratory
1 Exercises

You
will be given copies of hydrographic date for a local lake.Each student should carry out the following morphometric calculations,
and answer the following questions.

A.
Lake Morphometry

1.
Calculate the mean (˛) and relative depths (zr) and
the ˛: zmax ratio for each lake. What do these values
tell about the shape of each lake? Examine the maps and consider the scale of
each in your answer. Based on the general relationship between mean depth and
biological productivity, what can you say about the productivity of different
trophic levels in these lakes?

2.
Using a ruler, measure the fetch (in km) and estimate the depth of the summer
thermocline (in m) for each lake. Remember to convert your fetch measurements to
km using the scale on the maps (which are in m).Do you think that these estimates are reasonable considering
the morphometry of each lake?

3.
Lake 239 has 4480 m of shoreline (L) and Lake 304 has 827 m of shoreline.
Calculate shoreline development ratios (DL) and comment on the
potential for littoral community development in each lake.

B.
Hypsographic Curves

1.
Use the area data on the bathymetric maps to plot a hypsographic curve for each
lake. The curves should show cumulative % area vs depth. Remember that the
x-axis is cumulative area and should be at the top of the curve while the y-axis
shows depth, beginning at the top and increasing downward.

2.
What do the hypsographic curves tell you about the bottom shape of each lake
basin?

3. If
rooted aquatic macrophytes grow to a height of 2 m in each lake, what portion
(%) of the total lake area can be considered the littoral zone? Are your values
consistent with your comments concerning shoreline development ratios in each
lake?

C.
Nutrient supply and Trophic Status

1.Lake
239 drains an area of 260 x 104 m2 and Lake 304 drains a land area of
33 x 104 m2. Schindler argued that lake productivity was proportional
to the ratio of (A0 + A0)/V. Calculate these ratios and
comment on the trophic status of each lake. Are these results what you expected
considering your comments based on the hypsographic curves and DLs for each
lake?

E.
Lake Productivity Assessment

1.
Lake
trophic status is a function of edaphic (nutrient supply, e.g., Schindler’s
ratio) and morphometric factors. Comment on this statement briefly, using the
parameters that you’ve calculated in the previous sections to support your
answer. Indicate which lake is the most productive and which is the least
productive. If some of your calculations produce contradictory interpretations,
try to explain how you might resolve the difficulty. NOTE: we are not asking for
a strict classification into oligotrophic or eutrophic; rather we want your
informed opinion as to what you would expect to find if you went to these lakes
and sampled them.

Any
graphs that you do for this course should be neat and well labeled (axes,
including units, and a caption explaining what the graph is about). Hard copies
from various graphics programs are acceptable but note that standard scientific labeling
conventions should be followed (e.g., if your program will not label the y-axis
vertically, you will have to do it by hand). Hand-drawn curves should be on
graph paper and a ruler must be used.

Show
your work for any calculations that you hand in for marking. We are interested
in how you arrive at your answer as much as the result itself. Submission of a
final answer only will not receive full marks for a question.